The proposed 3D localization system
requires only a small amount of bandwidth without any demand for wideband implementation. For the angular parameter estimation, we leverage the channel sparsity at mmWave frequencies, in the form of rank deficiency of its autocorrelation matrix, and use off-grid Atomic Norm Minimization (ANM) [1]}, [2]} in conjunction with subspace-based root MUltiple SIgnal Classification (MUSIC) [3]} to extract the AoAs of the LoS channel path at each R-RIS subarray. Thanks to the similar path loss and received Signal-to-Noise Ratio (SNR), all the angular estimates possess similar performance in terms of the estimation error variance. Thus, for the mapping from the AoA estimates to the 3D coordinate of the MS, a Least Squares (LS) approachIn general, if the error variance for the estimation at each R-RIS subarray differs, a weighted LS will offer better performance compared to its unweighted counterpart. However, in all investigated cases in this paper, the error variances for the AoA estimates are approximately equal, thus, the weight matrix is in the form of a scaled identity matrix. In this sense, the weighted LS offers the same solution with the classical LS. is sufficient. Our derived theoretical Cramér Rao Lower Bounds (CRLBs) and simulated performance evaluation results showcase that the proposed R-RIS-based single-anchor 3D localization system can achieve cm-level estimation accuracy. In addition, we investigate the impact of the training overhead, MS-to-R-RIS distance, inter R-RIS subarray spacing, and the R-RIS partitioning patterns on the localization performance, offering useful insights for the practical deployment of the proposed system. The contributions of this paper are summarized as follows:
